Forward $\chi^2$ Divergence Based Variational Importance Sampling

• URL: http://arxiv.org/abs/2311.02516v2
• Date: Fri, 2 Feb 2024 09:46:20 GMT
• Title: Forward $\chi^2$ Divergence Based Variational Importance Sampling
• Authors: Chengrui Li, Yule Wang, Weihan Li and Anqi Wu
• Abstract summary: We introduce a novel variational importance sampling (VIS) approach that directly estimates and maximizes the log-likelihood. We apply VIS to various popular latent variable models, including mixture models, variational auto-encoders, and partially observable generalized linear models.
• Score: 2.841087763205822
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Maximizing the log-likelihood is a crucial aspect of learning latent variable models, and variational inference (VI) stands as the commonly adopted method. However, VI can encounter challenges in achieving a high log-likelihood when dealing with complicated posterior distributions. In response to this limitation, we introduce a novel variational importance sampling (VIS) approach that directly estimates and maximizes the log-likelihood. VIS leverages the optimal proposal distribution, achieved by minimizing the forward $\chi^2$ divergence, to enhance log-likelihood estimation. We apply VIS to various popular latent variable models, including mixture models, variational auto-encoders, and partially observable generalized linear models. Results demonstrate that our approach consistently outperforms state-of-the-art baselines, both in terms of log-likelihood and model parameter estimation.

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